Question

One number is twice another. The sum of their reciprocals is 3/2 . Find the numbers.

Answer 1

The two numbers are 1 and 2.

Explanation:

Let the two numbers be a and b.

One number is twice another, so let's let b=2a.

Their reciprocals are 3/2. Thus:

`(1)/(a)+(1)/(b) =(3)/(2)`

Substitute and solve for a:

`(1)/(a)+(1)/(2a) =(3)/(2)\\`

Combine the fractions by forming a common denominator by multiplying the left term by 2:

`(2)/(2a) +(1)/(2a)=(3)/(2)`

Combine and cross-multiply:

`3/2a=3/2\\6a=6\\a=1\\b=2(1)=2`

Thus, the two numbers are 1 and 2.